Fowl Mastermind here.
The answer is simple biology. Artemis, Juliet and Butler are all humans [known as 'mud men' to the People]. Whereas the good Lieutenant Cudgeon was an elf. We can simply theorize that none of the People can escape a time stop, and that time stops only affect sleeping mud men-- especially since the magic was used in the past to deter mud men from intervening on fairy business [they hint about the elf and cobbler tale].
Another answer could be the fact that none of the People can leave a time stop until it ends due to their magic. Remember, though the generators for the time stop are technological, they are still using fairy magic.
TLDR; he didn't poof cuz he's a magic jerkwad.